Question

The frequency driving an open-closed tube is steadily raised. Resonances are heard at 500 hz and 700 hz with none in between. What is the fundamental and next highest harmonic frequency?

Answer 1

The fundamental frequency is 500 Hz and the next highest harmonic is 1,500 Hz.

How to calculate the fundamental and harmonic frequency?

The lowest resonant frequency is called the fundamental, while all higher resonant frequencies are called overtones.

In an open-closed tube, the formula for each harmonic is given as;

f₀ = v/4L

where;

• L is the length of the tube
• v is the speed of sound

f₁ = 3f₀

f₂ = 5f₀, etc

From the given frequencies, the lowest frequency at which resonance is heard = 500 Hz (this is the fundamental frequency).

Next highest harmonic = 3f₀

= 3 x 500 Hz

= 1,500 Hz

Answer 2

Step-by-step explanation:

Frequency for a Open-closed tube is given by

`f=(2n+1)(V)/(4L)`

n=0 for Fundamental frequency

`f_0=(V)/(4L)`

the Next higher frequency

`f_1=(2* 1+1)(V)/(4L)=(3V)/(4L)`

`f_1=3f_0`

also

`((2n+1)(V)/(4L))/((2n+3)(V)/(4L))=(500)/(700)`

`(2n+1)/(2n+3)=(5)/(7)`

`14n+7=10n+15`

`n=2`

thus
`(V)/(4L)=100 Hz`

Therefore basic fundamental frequency is 100 Hz

and next highest harmonic frequency is

`f_1=3f_0=3* 100=300 Hz`